Traverse-table.



A. B. MITCHELL.

TRAVERSE TABLE.

APPLICATION FILED JULY 25,19I0. 1,232,706. Patented July 10, 1917.,

ARTHUR B. lVIITCI-IELL, OF BIRMINGHAM, ALABAMA.

TRAVERSE-TABLE.

Application led July 25, 1910.

To all whom t may concern:

Be it known that l, AirrnUn B. MITCHELL, citizen of the United States,residing at Birmingham, in the county of Jefferson and State of Alabama,have invented new and useful improvements in 'l`raverse-'I`ables, ofwhich the following is a specification.

My invention relates to improvements in a book of calculating tables foruse in determining the latitudes and departures, the noi-things orsouthings and castings or Westings, or cosines and sines, respectively,of bearings, courses, angles, or arcs, as the case may be, and comprisesdata Whereby the aforesaid functions may be readily and accuratelyascertained for any distance.

rThe primary object of a traverse table being to determine with theleast amount of time and labor the position of any point, of a definedangular course and distance from the point of beginning of a course, andto shon its relative position either horizontally or perpendicularly, orboth from such beginning point. Various forms of such tables have beenfrom time to time devised whereby relative perpendicular and horizontaldistances have been found for each angle of the quadrant by multiplyingthe natural sine or cosine of each angle by the tabular distances andthe results thus obtained then set down in horizontal or verticalcolumns, according to the inclination of the inventor, and referred toby appropriate reference numerals corresponding to such tabulardistances.

A traverse table extensively used by mathematicians and engineerscomprises a volume of 270 full pages devoted to traverse tables alone,requiring pages fourteen inches long and nine inches in Width, threepages are required representing the data concerning each degree, thedistances are disposed in horizontal columns reading downward from l to100 and the minutes of the angle or are arranged vertically. One-half ofeach page is devoted to cosines consisting of 10 vertical columnsshowing 10 minutes of a given degree, the other half of the page showingin the same manner the corresponding sines.

Another traverse table used arranges the distances in vertical columns lto 10, and minutes reading horizontally, with cosines and sines both inparallel columns and referred to by and disposed vertically under thesame gures used to designate distances.

Specification of Letters Patent.

Patented July 10, 191'?.

seriai No. 573,788.

These books of traverse tables, by reason of their employment of theadditional or lo column for distances are necessarily larger, requiringmuch more space in carrying, and are incapable of being suliicientlyreduced in size in their present form, to eli'ect a pocket edition, andstill preserve itsI legibility, unless their accuracy is materiallyaffected by reducing the number of decimal points to which the data iscarried.

None of the traverse tables coming within the scope of my observationhave extended their calculations to more than live decimal places.

The main object of my invention is to so arrange the data comprised inmy book of tables that the information sought shall be clearly distinctand quickly obvious, revealing the fullest amount of such information inthe most compact and legible form. It is my purpose to present the datain a volume having but ninety pages and Which ivill t into the pocket ofa coat or like receptacle or, in other Words, be of What is generallyknown as pocket edition size for convenience in ield use. Thepresentation of data is thus limited by tn'o factors, viz: the number ofpages and the size of the page, and in addition thereto the matter ofconvenient use requires that the data be printed large enough to bereadily legible, and arranged so that there will be but little chance oferror in selecting data from the tables. According to my invention Ipropose to present the tables in a pocket edition using numbers carriedto a greater number of decimal places than is customary in similartables now in use, thereby increasing the accuracy of the tables; topresent such numbers in type large enough to be easily legible; toarrange all the data for one degree of a quadrant relating to latitudeson one page and departures on the opposite page, making only ninetypages in the tables; to present the latitudes for a given degree on onepage and the departures for said degree on the opposite page; and whatis most important, to present all said data on pocket size pages byeliminating all superfluous data comprised in other tables, andutilizing the space thus obtained to increase the accuracy of my tablesbut not the size of the book.

One advantage of my invention is by my arrangement of the data so thatthe latitude, northing or southing, or cosine of any angle,

arc or bearing for every minute of the same the confusion incident toother systems where companion columns for both latitudes, etc., anddepartures, etc., are shown on the same page.

Another advantage oi" my invention is that the information sought forany angle, arc or bearing, is clearly shown on the same horizontal lineopposite the minutes in the vertical column or the minutes on the pageshowing the given degree of angle, etc.

This arrangement being effected by pre- Senting first the latitudes onone page and departures of the same angles on the opposite page at thetop of the page, reading from the beginning of the tables or 0D to theend of same or ao, thus the latitudes and departures for 450 or one-haltof the quadrant are presented, and, as the differences between 900 andthe angles and their func-V tions presented are respectively thecomplemental angles and functions of the quadrant therefore thelatitudes and departures, cosine and sine, etc., are found for remainingangles of the quadrant 450 to 90O by reading from the end of the tablesfrom right to left across the bottom toward the beginning in reverseorder. riChat is the pages sho-wing latitude at top of pages will showdeparture at the bottom of same page, which will be the departure forangle repjresenting the difference between the angle at top of page and900.

Another advantage or my invention is th reduction and limitation ot thenumber of columns containing' distances to nine (9) or one for each ofthe nine digits, where other systems show various arrangements or" tenor more columns.

These and other advantages which are devised from the arrangement andcombination of data in my present bool; of traverse tables are morefully hereinafter described, reference being had to the accompanying`drawing, wherein the figure indicates my improved bool; of traversetables open so as t0 show one page of latitudes, etc., of angle at thetop of the page and the departures7 etc., of the complement angle at thebottom of the same page, and another page of the book showing thedepartures, etc., of a different angle atthe top of the page and thelatitudes, etc., of the complement angle at the bottom of the same page.

According to the drawing the book coinprises essentially ninety pages lcorresponding to the 90o of the trigonometrical quadrant, and asuilticient number of explanatory pages may be added, there appearing tobe eight in this instance, and the book therefor-e is opened on pages 3Sand 69, the latitudes,

Y inclusive.

etc., or the angles, arcs, or bearings of 150 to 1GO and the departures,etc., or the corresponding complement angles, etc., 7a2@ to 750.r-ippearing on page 38, the departures, etc., for l5O to 1GO wouldappear as reading from the top downward on page 39 if shown,

the left by the numerals i'rom O to (50 inclusive, reading downward, andare headed at their right hand ends by theV saine numerals readingupward. rIhese two rows of numerals are arranged in vertical columns 3and l, the column 3 being headed at the top by the abbreviation M forminutes and the column L1 being headed at the bottom by the sameabbreviation M 'Between the columns 3 and e the sheet is divided intonine vertical columns headed at the top and bottom by the numerals fromto 9, inclusive, reading from left to right. The left hand pages attheir tops are each headed by the wort Latitudes and at their bottoms bythe word Departures At the pper left hand corner or' the page the degreeto which the data on that page, relative to latitudes pertains, isindicated by insertinO a given degree and also the succeeding degree, asfor instance, 15o to 16o, indicating that the page will contain all datarelating to an angle from 150 to 160, both The pages are marked at theirupper left hand end by the word Cosme and at the bottom of the columns 5by the word Sine, there appearing at the lower right hand corner or thepage the complementary angles to the angles appearinef at the upper lefthand corner, or in other words, the page illustrated shows angles from15o to 1GO and 74o to 75o, the minutes for intermediate angles from 150to 16 being read downwardly in the column 3 and from 74:0 to 75o beingread upwardly in the column (Je. rhe right hand pages are each headed bythe word Departures at the top and by the word Latitudes at the bottom.The degree to which the data pertains are indicated in the same way asin the case of the left hand pages, the word Sine appearing at the topof the columns 5 and the word Cosme appearing at the bottom. The wordscosine and latitudes are corresponding expressions as are sines anddepartures The vertical columns 1 to 9 shown at the top and bottom ofthe page are used to represent distances, which whenused in combinationcan be made to express any distance from naught (0) to innity, it beingobvious that the expression can be easily made by moving the decimalpoint as many places to the right as there are gures in the whole numberloss one, and, on the other hand to express a decimal quantity, thedecimal point is moved as many places to the lett as there are multiplesot ten in the division, the intervening places between the decimal pointand the first digit to the right of it being filled in with ciphers.

In column 5, which is headed l on each page of the tables appear thenatural cosines ot the angles, arcs or bearings shown on the pagereading downward on the lett hand pages and upward on the right handpages, while the corresponding natural sines are found in the same.column by reading from the bottom upward on the left hand page and fromtop downward on the right hand page. The other columns 5 head 2 3 etc.,to 9, represent, respectively, 2, 3, etc., to nine times the naturalcosines and sines as next above described. In the vertical columns 5 theirst three numerals, were duplicates of a preceding number, readingdownwardly are not repeated, but in using the table vthey will be readin with the succeeding tour numerals ot the number, as on page 38. Inthe vertical columns headed l the expression for the angle of l5O l is.9658505 and on page 69 the expression for the angle of 590 l is .MTSSTit will be noted that carry out the expressions in my table to sevendecimal points which gives great accuracy, particularly in makingcalculations for long courses. The expressions may be carried to alesser number ot' decimals it desired, but obviously the greater numberof decimal places to which the expressions can be carried withoutsacriicing legibility or increasing the size of the page, the moredesirable the tables will be.

While have stated that the data on each page is arranged in sixty-onehorizontal columns, the horizontal lines dening these columns need notnecessarily be shown. I prefer to use spaced horizontal lines betweengroups of horizontal columns 2 of data to assist in guiding the eye asit follows the columns across the page. As shown one of these linesappears below each .tilfth column 2 except at the bottom of the pagewhere six columns 2 are grouped. Also the more important advantagesderived trom my method ot presenting the data will be securedirrespective of whether each page shows the calculations for both thecolumns '2 headed O7 and 60, as one or the other ot these columns ofdata would be available on the preceding or succeeding page oitnlatitudes or departures, as the case may be.

Having thus described my invention, what l claim as new and desire tosecure by Letters Patent, is

l. As an article of manufacture, a pocket edition book of traversetables comprising pages ot tables, all data pertaining to the angles andcomplementary angles 'tor the minutes intervening between a given degreeand the succeeding degree being arranged on a pair of oppositely t'acingpages, the data tor latitudes being disclosed on one page and fordepartures on the opposite page of each pair, each page having the datathereon arranged in horizontal columns successively headed at the lettby the numerals from O to 60 reading down and headed at the right by thesame numerals reading from the bottom up, all the data on a page beingdisposed in only nine vertical juxtaposed columns, which nine verticalcolumns contain tabulated data and from left to right are headed by thenine digits, each page for latitudes or departures successively bearingindicia at its top showing the same angle to which the data thereon asread downwardly pertains and its bottom bearing indicia designating thecomplementary angle to that indicated by the indicia at the top of thepages.

2. ris an article oi manufacture, a bool; "et traversetables comprisingpages, of a size adapted for pocket use, there being a series ot pairsof oppositely facing pages, each pair of pages containing all datapertaining to the angles and complementary angles for the minutesintervening between a given degree and the succeeding degree, therebeing indicia designating said degree which is displayed at the top ofeach page ot a pair and indicia displayed at the bottom ot the pageindicating the complementary degree to that displayed by the indicia atthe top otl the page, all data pertaining to latitudes being arranged ona correspond ing page of each pair and the data pertaining to departuresbeing arranged on the other and corresponding pages ot said pairs, saidpages having the data arranged thereon in sixty-one horizontal columnsand being ruled at each side to torni avertical column, the column atthe lett at its top and the column at the right at its bottom beingmarked to indicate minutes, said horizontal columns of data being headedby numerals from O to 60 in said minute columns, said numerals beingarranged in numerical order as read downwardly on the lett and beingreversed and as read upwardly on the right, also each page being ruledinto only nine vertical juxtaposed columns headed by a digit, the frontcolumn on the left being headed by 1, the second by 2, etc., and thelast by 9, and said data, presenting calculations carried out to morethan i'ive decimal places, appropriately arranged in said verticalcolumns.

3. As an article of manufacture, a book of traverse tables condensed, aplurality of pages of tabulated data, each pair of oppositely facingpages having the data displayed thereon as read downwardly for theangles of one degree between 0O to` 4150, and the data on each pair ofpages as read upwardly being for the angles of the degree which iscomplementary to the degree with reference to which the data is readabledownwardly, there being appropriate degrees displayed at the top andbottom of each pair of pages to indicate the degrees as read downwardlyor upwardly to which the data thereon pertains, there being only ninevertical columns of data arranged on each page and all the datapertaining to latitudes being arranged on a corresponding page of eachpair and the data relating to' departures being displayed upon the otherpage of each pair, said Vertical columns of data having digits at theirtops from l7 to 9 successively reading from left to right, and the datasaid vertical columns being arranged in horizontal columns headed attheir left by minutes or the degree displayed at the top of the page andbeing headed at their right hand ends by the minutes or the degreedisplayed at their bottom and read from the bottom upward, the corresponding horizontal columns of data relating to latitudes anddeparturesv for a given minute of a degree being arranged in transyerse'alinein'ent in the oppositely facing pair horizontal and verticalcolumns, there be ing appropriate designations for minutes of a degreelheading the horizontal columns, similarly headed horizontal columnsbeing disposed in alinement across a pair or op positely facing pages,the vertical columns on each page being similarly headed by the digitsVfrom one up, and all data relating to latitudes for a given angle beingdisplayed in the columns of one page and the data relating to departuresfrom the same angle being displayed in the columns of the opposite page,substantially as described.

In testimony whereof I have hereunto set my hand in presence of twosubscribing witnesses.

ARTHUR B. MITCHELL. lVitnesses S. F. FosHEE, NOM'IE W'EilsHl Copies of'thspatent may be obtained for ve cents each, by addressing theCommissioner of Patents, washington, D. c.

